Numerical Methods

Numerical simulations have become an invaluable tool to study
the formation of stars. Highly non-linear interactions
(e.g. self-gravity and turbulence) and the complex physics
(e.g. chemistry and radiative processes), which are essential
to understand the assembly of stars, reduces analytic studies
to important but simple models. On the other hand, star
formation spans many orders of magnitudes in length scale
(from parsec size clouds to solar objects), which can not be
simulated on a static grid. In our research group we are using
two different approaches to overcome this barrier: smooth
particle hydrodynamics (SPH) and an adaptive mesh refinement
(AMR) grid code.

SPH: Smooth Particle Hydrodynamics

SPH is a Lagrangian method in which the fluid properties
are carried by a population of particles which are free to
move under the forces they experience from their surrounding
neighbours. The Lagrangian nature of the method means that
regions of high denisty are automatically higher resolved
than regions of low density. With this powerful technique, one
can study many orders of magnitude in the fluid properties.
For non-magnetic applications,
such as the gravitational fragmentation, collapse and evolution of a
molecular cloud, this is highly advantageous, and hence SPH has enjoyed
wide-spread use in the study of star formation. The lack of preferred
geometry in SPH also makes is idea for studying situations where
angular momentum transport and/or vector evolution is crucial.

AMR: Adaptive Mesh Refinement grid code

AMR codes are based on grid code techniques where the
fluid equations are solved using a
finite difference scheme. Additionally, AMR codes are able to
increase the resolution dynamically wherever necessary by
including higher refinement regions during runtime. Typically
this results in a patchwork of high and low resolution regions
within the simulation box. Examples of grid codes with AMR
technique are ENZO which is
used for cosmological simulations (Abel 2002), RAMSES,
NIRVANA,
and FLASH which
is used by our research group (e.g. Banerjee et al. 2006)

The figure shows an example of the grid structure, done with the
FLASH code, where a density refinement criterion is
applied. High density regions (central region) are resolved
with a finer spatial resolution than lower density ones.

The figure shows an example of the grid structure (done with the
FLASH code) where a density refinement criterion is
applied. High density regions (central region) are resolved
with a finer spatial resolution than lower ones.

Computing Facilities

Our work makes use of a number of national computing facilities, as
well as local facilities here in Heidelberg and at the
AIP (Postdam).
The homepages for the national facilities are listed below.